Question: Solve for $x$ : $ 6|x - 7| + 9 = -4|x - 7| + 7 $
Solution: Add $ {4|x - 7|} $ to both sides: $ \begin{eqnarray} 6|x - 7| + 9 &=& -4|x - 7| + 7 \\ \\ { + 4|x - 7|} && { + 4|x - 7|} \\ \\ 10|x - 7| + 9 &=& 7 \end{eqnarray} $ Subtract ${9}$ from both sides: $ \begin{eqnarray} 10|x - 7| + 9 &=& 7 \\ \\ { - 9} &=& { - 9} \\ \\ 10|x - 7| &=& -2 \end{eqnarray} $ Divide both sides by ${10}$ $ \dfrac{10|x - 7|} {{10}} = \dfrac{-2} {{10}} $ Simplify: $ |x - 7| = -\dfrac{1}{5}$ The absolute value cannot be negative. Therefore, there is no solution.